Dyon Death Eaters

TL;DR

This work derives a general master equation for marginal stability in two-body decays of 1/4-BPS dyons in type IIB on K3×T^2, extending Sen's circle to a broader class of decays and connecting the geometry of marginal walls to Farey sequences and Ford circles. It shows that decays into 1/2- or 1/4-BPS products correspond to distinct circle-like loci in the torus moduli space, with primitive and non-primitive dyons exhibiting different intersection properties in the upper half-plane. The authors reproduce Sen's results as a special case, generalise to non-primitive dyons, and reveal codimension-2 marginal loci when decays involve two 1/4-BPS dyons, offering insights into the counting of dyons and potential links to higher-genus structures in the BPS spectrum. Overall, the paper provides a unified, geometry-driven framework for understanding dyonic marginal stability with potential implications for black hole degeneracies and microstate counting in string theory.

Abstract

We study general two-body decays of primitive and non-primitive 1/4-BPS dyons in four-dimensional type IIB string compactifications. We find a ``master equation'' for marginal stability that generalises the curve found by Sen for half-BPS decay, and analyse this equation in a variety of cases including decays to 1/4-BPS products. For half-BPS decays, an interesting and useful relation is exhibited between walls of marginal stability and the mathematics of Farey sequences and Ford circles. We exhibit an example in which two curves of marginal stability intersect in the interior of moduli space.